There's no reason BitBucket, GitLab, and GitHub couldn't scan all of the unmerged commits on pushed branches to look for impending merge conflicts. BitBucket at least does once you start a PR. They could be more aggressive about that without changing any underlying algorithms.

The main difference would be that the PR check only compares with master, and you'd want to compare all branches. But a low-constant-factor test for collisions would make that cheap enough (conflicts can only occur for commits that contain the same file names, which is an O(mlogm) set intersection test of short text strings)